We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset Hq,n of the variety of (q+n)-dimensional Lie algebras, parameterizing ...

In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the omega-limit of bracket ...

This paper is concerned with Chern-Ricci flow evolution of left-invariant hermitian structures on Lie groups. We study the behavior of a solution, as t is approaching the first time singularity, by rescaling in order to ...

We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci ...

First, we introduce the basic concept of minimal surfaces and develop some results in the general theory of minimal surfaces. In the second part, we are interested in the Simon-Smith Min-Max approach to prove the existence ...

In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, ...

Nesta dissertação, será apresentado um estudo sobre o princípio do máximo para escalares e fibrados vetoriais sobre variedades compactas e algumas aplicações sobre o fluxo de Ricci, tendo como objetivo final demonstrar ...